1. Technical Field
The present invention relates to a vibratory sensor detecting a change in a resonance frequency of a piezoelectric resonator element occurring due to a force exerted by acceleration or the like.
2. Related Art
There is a vibratory sensor known as a force sensor measuring a force generated by acceleration or the like. The vibratory sensor detects a magnitude of the force by detecting a change in the resonance frequency of a piezoelectric resonator element occurring due to the force exerted by the acceleration or the like (e.g. See JP-T-40505509 (FIG. 1) and “Force Sensing Using Quartz Crystal Fexure Resonators”, 38th Annual Frequency Control Symposium 1984, pp 233-239, by W. C. Albert).
Hereinafter, a structure of an acceleration sensor as an example of the vibratory sensor will be described. FIG. 6 is a perspective view schematically showing a conventional acceleration sensor. As shown in FIG. 6, an acceleration sensor 500 includes two connection boards 102, 103 formed on a base 101, and a resonator element 100 connected to the connection boards 102 and 103. The resonator element 100 is made of a piezoelectric material such as quartz crystal. The resonator element 100 includes resonating arms 105, 106 formed by splitting by a through-hole 104, and two base portions 107 and 108 extended from opposite ends of the resonating arms 105 and 106.
Now, detection of acceleration will be briefly described by using an example in which acceleration in a thickness direction (a P direction) of the resonator element 100 is exerted to the acceleration sensor 500. Due to acceleration exerted on the acceleration sensor 500, the base 101 bends by movement of a second base portion 101a of the second base 108 in a rotating direction around a hinge 109 as a fulcrum formed on the base 101. The acceleration sensor 500 detects a change in the resonance frequency caused by deformation of the resonating arms 105 and 106 occurring by the bending, thereby measuring a magnitude of the acceleration exerted. In this case, detection sensitivity is represented by a following formula (1). The formula (1) shows that the detection sensitivity becomes higher as a resonating arm length l becomes longer.
                              Formula          ⁢                                          ⁢          1                ⁢                                                                                                Δ          ⁢                                          ⁢          f                =                              a            t                    ⁢                                    mal              2                                      Etw              3                                                          (        1        )            
In the formula, a1 represents a constant number determined by support or the like; m represents a mass; a represents acceleration; E represents an elastic constant; l represents a resonating arm length; t represents a resonator element thickness; and w represents a resonating arm width.
Vibration leaking from the resonating arms 105 and 106 is transmitted to the first and the second base portions 107 and 108. The leaking vibration reduces a Q value of the resonator element 100, thereby causing resonance frequency variation. Accordingly, the acceleration cannot be detected with high precision. Thus, to suppress such vibration leakage, there is proposed an acceleration sensor as shown in FIG. 7 (e.g. See JP-A-63-284440 (FIG. 4)). FIG. 7 is a plan view of a conventional resonator element used in the acceleration sensor.
As shown in FIG. 7, in a resonator element 200, there are integrally formed a pair of resonating arms 205, 206, a first base portion 207 and a second base portion 208 as two base portions, first narrow portions 209, second narrow portions 210, and support portions 211, 212. The resonating arms 205 and 206 are two beam-shaped portions formed by splitting by a through-hole 204. Opposite ends of the resonating arms 205 and 206 in an extending direction of the arms (a longitudinal direction) are extended to the first base portion 207 and the second base portion 208. The first and the second base portions 207 and 208, respectively, are extended in the extending direction of the resonating arms 205 and 206. The first base portion 207 has the first narrowed portions 209 where grooves are formed by providing a cutting at opposite ends such that a part of the first base portion 207 has a two-dimensionally small width. Similarly, the second base portion 208 has the second narrowed portions 210 with grooves formed by providing a cutting at opposite ends such that a part of the second base portion 208 has a two-dimensionally small width. In this case, a direction orthogonal to the extending direction of the resonating arms 205, 206 is equivalent to a width direction, and a length of the width direction is referred to as a width. Furthermore, at one side of the first base portion 207 is formed the support portion 211, whereas at one side of the second base portion 208 is formed the support portion 212. Forming the first and the second narrowed portions 209 and 210 can suppress leakage of vibration of the resonating arms 205 and 206 to the support portions 211 and 212.
However, in the acceleration sensor using the above-described resonator element 200, a length L of each of the first and the second narrowed portions 209 and 210 is made short. Accordingly, stress induced by a shock or the like imparted to the acceleration sensor is concentrated on the first and the second narrowed portions 209 and 210, whereby the resonator element 200 can have damage to the narrowed portions 209 and 210, and thus, acceleration detection is impossible. Particularly, when the acceleration sensor 500 of FIG. 6 uses the resonator element 200 of FIG. 7 instead of the resonator element 100, a force bending in the P direction is applied to the first and the second base portions 207 and 208. Then, for example, stress induced by the bending force tends to be concentrated on the narrowed portions 209 less rigid than the first base portion 207 (namely, on a neck portion between the two narrowed portions 209). Thus, when the length L of the narrowed portions 209 is short, stress is concentrated locally on the narrow region, and thereby, a large bending force occurs at the neck portion. Additionally, the narrowed portions 209 tend to be cut ends, thereby causing damage to the resonator element 100.